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Quadratic equations and the relationships between lines, such as parallel and perpendicular lines, are fundamental concepts in algebra and geometry. This guide will walk you through the steps to solve quadratic equations using the quadratic formula, find X and Y intercepts, graph parabolas, and understand the properties of parallel and perpendicular lines. Solving Quadratic Equations with the Quadratic Formula The quadratic formula is a powerful tool for solving quadratic equations of the form a x 2 + b x + c = 0 ax^2 + bx + c = 0 . The formula is: x = − b ± b 2 − 4 a c 2 a x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ​ Steps to Solve for X Intercepts Identify Coefficients : Determine the values of a a , b b , and c c  from the quadratic equation. Plug into the Quadratic Formula : Substitute these values into the quadratic formula. Calculate : Perform the arithmetic operations to find the solutions for x x . Find X Intercepts : The solutions for x x  are the X intercepts, where the ...